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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 28, page id 797435492:0048
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L F C Y. III.
Tumatur utcunque punctum R; et ab eo ducta R L ad perpendicularem
C. N parallela cum incidenre conveniet ad L, erit illic K N =NL, ie
hicKH. NL:: I. R.)
Nam F. inredectione; quoniani ang. OPYC ==RNTC (ex lege
retlectionis.) Ft ang. O NC = =R C. N (ex HIyporheli quod ON.
C B Parallela sunc) erit ars. A CN = ans. RNI C. adeoque RH
=RC =NL: O. F. D.
2 Inretractione; ducantur C F ad NO, _ CF ad NR perpen-
diculares (unde liquer puncta F, F existere in circulo super diametrum
C N descripro) quare, connexa FF; crunt anguli C PF = ang.
FNC (eidem insistentes peripheriae FC) aquales. Item proprerca
est ang. F C F = ang. F N F = ang. NVR C. quare triangula F C F,
NR C sunc aequiangula sibi mutuo; quamobrem est C F. C P::
R N. R C. atqui (juxta legem retractionis) est C. F. C F:: I. R.
qua propter erit, RH.. KC:: I. R: vel RN. N L:: P, R:
L. F. D.
XI. Ouod si per N ducatur tangens V F; erit (in reflectione) eti-
a R T = RN; _ NT angulum M N R bilecabit. In retracti.
OREVeTO CrIER P ad R N, ut co sinus anguli retracti, ad colinum an-
suli incidentix. Oux Palrem ad noto, ceu Lemmarica.
XII. Exhis Facile deducantur Conicarum Sectionum circa radiorum
inflectionem latis jam perrulsatae proprietates; at qua Forcasse per
nimias ambases.
+. Demonstrarx prostant. Uc in parabola (puta R B S, cujus axis
B C) incidat M NO axi B C parallelus; ejusque reserus (IENR;
erit igitur (ex OstensIs) RNI = R C. aE SI punCtuM R ponatur umbi-
licus parabolx; erit eriam inde (juxta norissimam hujusce currx pro-
Prietatem) RN = RC. quare paralleli radii retlexus neceslario
per umbilicum eransibit; qui proxterea non immerito quoque focus
appellatur.
2. Item in ellipse, cujus axis BD, Foci H, R, SI ad quodvis curree
punctum N a Focis ducantur rectae HN, RN; Caris celebre est, quod
perpendicularis C N angulum HINR Bilecabit. Unde NH. NK::
HIC. CK. _ componendo N HI F NK. NR:: HIR. CR. vel BD.
NK:: FIK. C R. vel permutando BD. HIR:: NR. CK. quare
Sitalis Tuerit ellip(IS, ut sIEBD. HIR:: I. R. Ctiam erit NR. CR::
l. R. verum (i incidens MI HI ad B D parallelus retringatur in. NR,
erir (juxta mox ostensa) etiam NK. CR:: L. R. Patet itaque quod
iplius M N retractus per focum R cransibir. Quid plura. 3
31
E18. 24, 251
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